View source for PhET/C2/Equation-Grapher/English

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|| '''Visual Cue'''
|| '''Narration'''

|-
|| '''Slide Number 1'''

'''Title Slide'''
|| Welcome to this tutorial on '''Equation Grapher'''.
|-
|| '''Slide Number 2'''

'''Learning Objectives'''

We will demonstrate '''PhET simulation''',

'''Equation Grapher'''
|| In this tutorial, we will demonstrate '''Equation Grapher PhET simulation'''.
|-
|| '''Slide Number 3'''

'''System Requirements'''

'''Ubuntu Linux OS''' version 16.04

'''Java''' version 1.8.0

'''Firefox Web Browser''' 60.0.02
|| Here I am using,

'''Ubuntu Linux OS''' version 16.04

'''Java''' version 1.8.0

'''Firefox Web Browser''' version 60.0.02
|-
|| '''Slide Number 4'''

'''Pre-requisites'''
|| Learner should be familiar with topics in high school mathematics.
|-
|| '''Slide Number 5'''

'''Learning Goals'''

Lines '''y = bx + c''' and '''y = c'''

'''Quadratic polynomials''' '''y = ax<sup>2</sup> + bx + c'''.

|| Using this '''simulation''' we will look at,

Lines of the form '''y = bx + c''' and '''y = c'''

'''Quadratic polynomials''' '''y equals ax squared plus bx plus c'''
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|| '''Slide Number 6'''

'''Binomial Theorem'''

'''Binomial theorem''' states that if ''a, b'' ∈ ℝ, index ''n'' is a positive integer, ''0 ≤ r ≤n, then,''

''(a + b)<sup>n</sup> <nowiki>= </nowiki><sup>n</sup>C<sub>0</sub> a<sup>n</sup> + <sup>n</sup>C<sub>1</sub> a<sup>n-1 </sup>b<sup>1</sup> + <sup>n</sup>C<sub>2</sub> a<sup>n-2 </sup>b<sup>2</sup> + … + <sup>n</sup>C<sub>r</sub> a<sup>n-r </sup>b<sup>r</sup> + … + <sup>n</sup>C<sub>n</sub> b<sup>n''</sup>

'''Reminder:''''' <sup>n</sup>C<sub>1</sub> = n!/[1! (n-1)!]''
|| '''Binomial Theorem'''

'''a''' and '''b''' are real numbers, '''index''' '''n''' is a positive integer.

'''r''' lies between 0 and '''n'''. 

Then, '''Binomial theorem''' states that '''a''' plus '''b''' raised to '''n''' can be expanded as shown.
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|| '''Slide Number 7'''

'''Link for PhET simulation'''

[http://phet.colorado.edu/ http://phet.colorado.edu]
|| Use the given link to download the simulation.

[http://phet.colorado.edu/ http://phet.colorado.edu]
|-
||
|| I have already downloaded '''Equation Grapher''' simulation to my '''Downloads''' folder.
|-
|| Press Ctrl+Alt+T to open the terminal.

Type '''cd Downloads''' >> press '''Enter'''.

Type '''java space hyphen jar space equation-grapher_en.jar'''.

Point to the opened '''file format'''.
|| To open the '''jar file''', open the '''terminal'''.

At the '''terminal prompt''', type '''cd Downloads''' and press '''Enter'''.

Type '''java space hyphen jar space equation-grapher_en.jar'''.

Press '''Enter'''.

'''File''' opens in the '''browser''' in '''html format'''.
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|| Cursor on the '''interface'''.
||This is the '''interface''' for the '''Equation Grapher simulation'''.
|-
|| Point to the '''interface'''.

|| The interface shows '''Cartesian co-ordinate system''' of '''x''' and '''y axes'''.
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|| Point to the first '''quadrant'''.

Point to the '''quadratic function''', '''y = ax<sup>2</sup> + bx + c'''.

Point to the '''sliders''' and '''display boxes'''.

Point to the red '''Zero''' button.

Point to the green '''Save''' button.

Point to the equation.
|| The first quadrant contains:

The red-colored '''quadratic equation''', '''y equals ax squared plus bx plus c'''

Three '''sliders''' and display boxes under '''ax<sup>2</sup>, bx''' and '''c'''

The '''sliders''' allow you to change the values of the coefficients, '''a''', '''b''' and '''c'''.

The display boxes show these values and can be used to enter values.

A red '''Zero''' button to set all '''sliders''' at '''0'''

A green '''Save''' button to save the '''equation'''

The updated equation in red is shown below the '''sliders'''.
|-
|| Point to the fourth quadrant.

Point to the '''quadratic equation'''.

Point to the check boxes.

Point to the violet, green and blue terms.

|| The fourth quadrant contains the

'''Quadratic''' equation '''y = ax<sup>2</sup>+bx+c'''

Three check boxes under '''ax<sup>2</sup>, bx''' and '''c'''

Note that the '''ax squared''' term is violet, '''bx''' is green and '''c''' is blue.
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|| In the first quadrant, in the display box below '''ax<sup>2'''</sup>, type 1.

Point to the '''slider''' under '''ax<sup>2'''</sup>.
|| In the first quadrant, in the display box below '''ax squared''', type 1.

Observe how the '''slider''' under '''ax squared''' also moves to 1.
|-
|| Point to the red parabola and origin '''(0,0)'''.
|| A red parabola with vertex at origin '''0 comma 0''' appears in the window.

It opens upwards.
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|| In the first quadrant, in the display box below '''bx''', type 1
|| In the first quadrant, in the display box below '''bx''', type 1.
|-
|| Point to the parabola.
|| Observe how the parabola shifts downwards and to the left.
|-
|| In the first quadrant, in the display box below '''c''', type 1.
|| In the first quadrant, in the display box below '''c''', type 1.
|-
|| Point to the parabola.
|| Observe how the parabola moves upwards.
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|| In the fourth quadrant, check the box below the violet coloured '''ax<sup>2'''</sup> term.
|| In the fourth quadrant, check the box below the violet coloured '''ax squared''' term.
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|| Point to the violet and red parabolas.

Point to the equation.
|| A violet parabola appears next to the red parabola.

This violet parabola corresponds to the '''y equals ax squared''' part of the red equation.
|-
|| Point to the equation, '''y = x<sup>2'''</sup>, in the first quadrant.
|| The equation for the violet parabola is '''y equals x squared'''.
|-
|| Check the box below the green '''bx''' term in the fourth quadrant.
|| Now, in the fourth quadrant, check the box below the green '''bx''' term.
|-
|| Point to the green line.

Point to the origin '''(0,0)'''.

Point to the equation, '''y = x''', in the first quadrant.
|| Observe how a green line appears in the '''Cartesian''' plane.

It passes through the origin '''0 comma 0'''.

It corresponds to the '''x''' term and its equation is '''y equals x'''.
|-
|| Check the box below the blue '''c''' term in the fourth quadrant.
|| Now, in the fourth quadrant,check the box below the blue '''c''' term .
|-
|| Point to the blue line.

Point to the equation, '''y=c'''.
|| Observe how a blue line appears in the '''Cartesian''' plane.

Its equation is '''y equals c''' and it corresponds to the constant term of the equation.
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|| Click on the green '''Save''' button.
|| Click on the green '''Save''' button.
|-
|| Point to the blue saved parabola, '''y = x<sup>2</sup>+ x + 1'''.
|| This saves the equation '''y equals x squared plus x plus 1'''.
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|| Change values for '''a''', '''b'''and '''c'''.

Point to the '''sliders''' and the display boxes below the terms.

Point to the graphs.
|| Change the values for '''a''', '''b''' and '''c'''.

You can either use the '''sliders''' or type in the display boxes below the terms.

Observe the effects of these changes on the graphs.
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|| Point to the blue saved parabola, '''y = x<sup>2</sup> + x + 1'''.
|| Note that as you change '''a''', '''b''' and '''c''', you can still see the parabola '''y equals x squared plus x plus 1'''.

This is because we saved this equation.
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||
|| Save other graphs that you want to compare to see the effects of '''a''', '''b ''' and '''c'''.

You can only save one equation at a time.
|-
|| Point to the blue '''Erase''' button.
|| Note that after you have saved an equation, a blue '''Erase''' button appears.

This will erase the saved equation.
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|| Click on the red '''Zero''' button.
|| Click on the red '''Zero''' button.

This resets all coefficients '''a''', '''b''' and '''c''' to 0.
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|| '''Slide Number 8'''

'''Assignment'''
|| As an '''assignment''', compare the parabolas graphed for different combinations of:

'''a''' <0 and '''a''' >0

'''b''' <0 and '''b''' >0

'''c''' <0 and '''c''' >0
|-
|| '''Slide Number 9'''

'''Summary'''
|| In this '''tutorial''', we have demonstrated the

'''Equation Grapher PhET simulation'''
|-
|| '''Slide Number 10'''

'''Summary'''
|| Using this '''simulation''', we have looked at:

Lines of the form '''y = bx + c''' and '''y = c'''

'''Quadratic polynomials''' '''y = ax<sup>2</sup> + bx + c'''
|-
|| '''Slide Number 11'''

'''About the Spoken Tutorial Project'''

Watch the video available at http://spoken-tutorial.org/ What_is_a_Spoken_Tutorial

It summarizes the Spoken Tutorial project

If you do not have good bandwidth, you can download and watch it
|| The video at the following link summarizes the '''Spoken Tutorial project'''.

Please download and watch it
|-
|| '''Slide Number 12'''

'''Spoken Tutorial workshops'''
|| The '''Spoken Tutorial Project''' team conducts workshops using spoken tutorials and gives certificates on passing online tests.

For more details, please write to us.
|-
|| '''Slide Number 13'''

'''Forum for specific questions:'''

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question

Explain your question briefly

Someone from our team will answer them
|| Please post your timed queries in this forum.
|-
|| '''Slide Number 14'''

'''Acknowledgement'''
|| This project is partially funded by '''Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching'''
|-
|| '''Slide Number 15'''

'''Acknowledgement'''
|| '''Spoken Tutorial Project''' is funded by '''NMEICT''', MHRD, Government of India.

More information on this mission is available at this link.
|-
||
|| This is '''Vidhya Iyer''' from '''IIT Bombay''' signing off.

Thank you for joining.
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